IJPAM: Volume 61, No. 2 (2010)


Silas N. Onyango$^1$, Naftali Omollo-Ongati$^2$, Nyakinda Joseph Otula$^3$
$^{1,2,3}$Department of Mathematics and Applied Statistics
Maseno University
P.O. Box 333, Maseno, KENYA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]
$^3$e-mail: [email protected]

Abstract.We introduce a type of Itô process that models the adjustment of the market price of a traded security to new information affecting supply and demand of an asset. It is based on supply and demand functions and the Walrasian price adjustment assumption that proportional price increase is driven by excess demand. When supply and demand curves are linearised about the equilibrium point, the process turns out to be a logistic form of Brownian motion with random element of the Wiener type. Finally we derive the modified Black-Scholes Merton partial differential equation.

Received: April 20, 2010

AMS Subject Classification: 60J65

Key Words and Phrases: excess demand function, Walrasian price adjustment process, logistic Brownian motion, black-scholes-merton partial differential equation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 61
Issue: 2